Fractal geometry: notes from Ghod

Dear Ghu! I saw the most amazing special on PBS last night. Program
about the Mandelbrot set. Included interviews with Mr. M hisownself, if
I'm not mistaken. (They didn't label him after I channel-surfed in, so
I'm not sure, but that must have been who it was.)

I tell you, the film editors must have been doing some serious drugs
while they put that thing together. There's an awful lot of fractal art
out there that bores me to tears, mainly because of the colors and the
composition used. But this stuff was very well done, with well-chosen
color schemes for the most part (though there were a couple of
sequences where I had to shut my eyes to head of oncoming seizures),
and they kept things moving well. Helped a lot that they used movies,
with the imagery evolving over time.

I'm fascinated by fractals, have been ever since I first heard about
them. I really need to sit down over coffee sometime with somebody who
speaks the language and have them walk me through it. Haven't been able
to follow the math from books 'cause it, as usual, puts me right to
sleep. But I am really curious about the relationships described....

They didn't quite come out and say it, but there seems to be a
largish body of evidence suggesting that humans are hardwired for
fractal geometry. They showed a collection of intricate, geometrical
art having fractal-like properties, including stained-glass church
windows, Persian rugs, and mandalas. (It was pointed out that the word
"mandala" and Mandelbrot's name have common origins, which is a
pleasingly spooky bit of synchronicity.) Furthermore, Mandelbrot
commented that, when he was working this stuff out, he didn't feel as
if he was inventing it, by any stretch. Rather, he said, it was
as if this stuff already existed, and he was just uncovering it.

What really set my hair on end, though, was that I just finished
re-reading Contact, wherein Sagan has the main character uncover
a direct message from God, in the form of a perfect circle described as
a raster graphic in binary notation, buried way down deep in the
decimals of pi (when rendered in base-11, and much farther in than
we've been able to compute to date, of course).

The point Sagan harps on repeatedly is that if God had wanted to prove
Her existence, couldn't She have done so in a clear and unambiguous
way? The thought that keeps crossing my mind is this: what if it's
there, but we just don't know how to read it yet? I mean, in the book
Sagan has his characters find a messages that's sort of the equivalent
of "See Spot Run," after going through all sorts of contortions to get
to it. But what if the message is written in the celestial equivalent
of C++? Don't matter how big your English vocabulary is.

That's what this fractal geometry business smells like to me. (Not to
mention all that non-coding stuff in the human genome.) Kinda sends
chills down my spine....